1. Field of the Invention
The present invention relates to an apparatus and a method for analyzing the blood-flow dynamics of a sample from image data of the sample obtained with medical diagnostic imaging apparatus such as a magnetic resonance imaging (MRI) scanner, an X-ray CT scanner, a single photon emission CT (SPECT) scanner, a positron emission CT (PET) scanner and, more particularly, it relates to an apparatus and a method for measuring blood-flow dynamics easily, quickly, and accurately using time-series continuous image data collected by applying a labeled substance which is called a tracer to the blood flow in the sample.
2. Description of the Related Art
In general, in dynamic study with an X-ray CT scanner or a dynamic susceptibility contrast MRI (DSC-MRI) with a magnetic resonance imaging scanner, as described in “Østergaard L, Sorensen A G, Kwong K K, Weisskoff R M, Gyldensted C, Rosen B R; High Resolution Measurement of Cerebral Blood Flow Using Intravascular Tracer Bolus Passages, Part II: Experimental Comparison and Preliminary Results, Magn Reson Med, 1996; 36:726-736” and “Østergaard L, Weisskoff R M, Chesler D A, Gyldensted C, Rosen B R; High Resolution Measurement of Cerebral Blood Flow Using Intravascular Tracer Bolus Passages, Part I: Mathematical Approach and Statistical Analysis. Magn Reson Med, 1996; 36:715-725,” a contrast medium is infused through a vein to collect time-series image data, and then the images are analyzed to express blood-flow parameters in numerical form or images. An example of the analysis procedure is shown in steps S1, S2, S3A, and S4A or steps S1, S2, S3B, and S4B of FIG. 8.
For quantification, deconvolution with the time intensity curve (TIC) of a measured tissue, Ci(t), is performed with the TIC of an artery flowing into the tissue as input function to eliminate variations in pulmonary circulation and medium infusion, thereby obtaining the residue function: Ri(t) specific to the tissue, from which parameters such as blood flow: Flow, which is the index of blood-flow dynamics (cerebral blood flow: CBF for brains), mean transit time: MTT, blood volume: Volume (cerebral blood volume: CBV for brains) are calculated.
Another example is, as described in “Radiology 1998; 209 85-93” and “Miles K et al., British Journal of Radiology, 1991; 337: 643-645,” a maximum gradient method of calculating Flow from the maximum gradient of tissue TIC: Ci(t) and the maximum value of Ca(t).
In general, only one of bilaterally symmetric organs, such as brains, kidneys, and lungs, often develops abnormality, in which case diseased organs or regions have been often compared to the other corresponding healthy organs or regions or relatively stable part of diseased organs up to now. The ratio to the healthy part (healthy-part ratio) or the difference from that (healthy-part difference) is used for comparison, which is limited only to the case of documentation in numerical form but not in image. Disease data is often stored in database as healthy-part ratio or healthy-part difference.
The principle and situation of conventional blood flow measurement including its problems will be described with reference to literature.
(Blood Flow Model)
FIG. 9 shows a blood flow model into which a contrast medium is applied. In the drawing, case 1 shows a case in which a bolus of a contrast medium is infused into an artery in the close vicinity of a tissue of the blood flow model, while case 2 shows a case in which the contrast medium is infused into a cubital vein.
The model of the blood flow is expressed mathematically asCi(t)=Ca(t)*Ri(t)=∫0TCa(T−t)Ri(t)dt  (1)where Ca(t) is an artery TIC, Ci(t) is a tissue TIC, Ri(t) is a tissue MTF (modulation transfer function), and * is convolution.
Particularly, when Ca(t)=δ(t), where δ(t) is a delta function, the blood flow is expressed asCi(t)=δ(t)*Ri(t)=Ri(t)  (2)Specifically, in case 1 in which a bolus of a contrast medium is infused into an artery in the close vicinity of a tissue, the tissue MTF: Ri(t) becomes Ci(t).
In the case of calculations of CBF, CBV, and MTT by the conventional deconvolution method, Ri(t) is obtained from Ca (t) and Ci (t), as shown in FIG. 8, from which the parameters are obtained by the equations
                                                        CBF              =                            ⁢                              max                ⁢                                                                  ⁢                                  of                  ⁢                                                                          [                                      Ri                    ⁡                                          (                      t                      )                                                        ]                                                                                                        CBV              =                            ⁢                                                ∫                  0                  ∞                                ⁢                                                      Ci                    ⁡                                          (                      t                      )                                                        ⁢                                                                          ⁢                                                            ⅆ                      t                                        /                                                                  ∫                        0                        ∞                                            ⁢                                                                        Ca                          ⁡                                                      (                            t                            )                                                                          ⁢                                                                                                  ⁢                                                  ⅆ                          t                                                                                                                                                                                            MTT              =                            ⁢                              CBV                /                CBF                                                                        (        3        )            
The conventional calculation method includes a case of measuring artery TIC and correcting tissue TIC with the artery TIC and a case of analyzing tissue TIC without measuring the artery TIC. In the former case, the absolute values of the blood flow parameters are obtained; in the latter case, relative indices which reflect the blood flow (depending on variations among individuals and the respiratory function) are obtained.
FIG. 10 shows a gamma function used in TIC analysis. The meanings of the parameters in the drawing are as follows:
a) PH: Peak Height
the maximum value of C(t) (T0≦t<Infinity)
b) PT: Peak Time
time from the base time to PH
c) AC: Area under Curve
an area under the fitting curve, which corresponds to rCBV
d) MT1: 1'st moment
time from the base time to the first moment (barycenter)
e) rFLOW: relative Flow
relative flow based on a centric volume theory, which includes effects of blurring in pulmonary circulation or an artery
f) TT: Transit Time
time between inflection points of PH with PT interposed therebetween (different from a full width at half maximum (FWHM))
g) AT: Appearance Time
time from the base time until C (t) rises to a value AAT times as high as PH (default: AAT=0.05)
h) DT: Disappearance Time
time from the peak time until C (t) falls to a value ADT times as high as PH (default: ADT=0.4)
i) MT2: 2'nd moment
the second moment of the time of TIC, which corresponds to dispersion and indicates the temporal dispersion of the curve
j) US: Up Slope
slope at a rising inflection point
k) DS: Down Slope.
slope at a falling inflection point
l) PTE: effective Peak Time
m) MT1E: effective 1'st moment, MT1E=MT1−AT
time after the arrival of a contrast medium to a barycenter, MT1 with delay time in pulmonary circulation excluded
n) rFLOWE: effective relative FLOW, rFlOWE=AC/MT1E
closer to the true flow, with delay time in pulmonary circulation excluded
When the respective Ca (t) of the arteries are different only in delay: Td (refer to FIG. 12), also the delay can be expressed as Ri(t−Td) in which Ri(t) contains Td.
Ri(t) can be obtained by the expression of FickdCi(t)/dt=f●{Ca(t)−Cv(t)}  (4)where Ci(t) is tissue TIC, Ca(t) is input artery TIC, Cv(t) is output vein TIC, and f is blood flow (flow rate in unit volume [ml/cc/sec])
and the integral is expressed as
                              Ci          ⁡                      (            t            )                          =                  f          ⁢                      {                                                            ∫                  0                  t                                ⁢                                                      Ca                    ⁡                                          (                      s                      )                                                        ⁢                                                                          ⁢                                      ⅆ                    s                                                              -                                                ∫                  0                  t                                ⁢                                                      Cv                    ⁡                                          (                                              s                        _                                            )                                                        ⁢                                                                          ⁢                                      ⅆ                    s                                                                        }                                              (        5        )            where, when Ca(t)=((t), Ci(t)=Ri(t) holds.
Accordingly, the following expression holds:
            ∫      0      t        ⁢                  δ        ⁡                  (          s          )                    ⁢                          ⁢              ⅆ        s              =      Ramp    ⁡          (      t      )      where Ramp(t)=1:t>0,=0: otherwise, therefore the following expression holds:
                              Ri          ⁡                      (            t            )                          =                  f          ⁢                      {                                          Ramp                ⁡                                  (                  t                  )                                            -                                                ∫                  0                  t                                ⁢                                                      Cv                    ⁡                                          (                      s                      )                                                        ⁢                                                                          ⁢                                      ⅆ                    s                                                                        }                                              (        6        )            
Unless artery TIC: Can(t) in the cross vicinity of the inflow of the object tissue is measured, true MTT cannot be calculated normally.
When a contrast medium is infused through a cubital vein (case 2), TIC: Ca(t) of an artery flowing into the tissue expands in terms of time owing to pulmonary circulation. Thus both tissue TIC: Ci(t) and vein TIC: Cv(t) expand as compared with case 1. The difference for positions of cerebral arteries after the contrast medium has flowed into a brain from a lung is only delay but the width is substantially fixed if arteries of different flow channels do not join together but branch off.
There can be several kinds of Ri(t) depending on the model of blood flow.
For example, in the case of a box model, Ri(t) is expressed asRi(t)=f: Td<t<Td+MTT,=0: otherwisefor an exponential model, Ri(t) is expressed asRi(t)=f*exp[−(t−Td)/MTT]:Td<t<Td+MTT,=0:otherwise(Relationship between Tissue MTT and Barycentric Time MT1)
Problems of using the barycenter time MT1 of the first pass of tissue TIC as index will be examined.
Although the time between the MT1 of Ca(t) and Cv(t) has no dependence to Ri(t), or the blood flow model, the MT1 of Ci(t) has dependence to the blood flow model. When tissue TIC: Ci(t) and any artery TIC: Ca(t) are measured, the following expression holds:MTT=a(MT1i−MT1a−Td)  (7)where MT1i and MT1a are the respective barycenters of the first passes thereof and Td (refer to FIG. 12) is the delay time from the measured artery to the inlet.
Where a is a coefficient which depends on the model and will fall within the range of 1≦a≦2. For a plug-flow contrast medium, the blood flow is of a box model in which a=2 holds; for a diffusion tracer, the blood flow is of an exponential model, in which a=1 holds.
Letting MT1v be the barycentric time for a vein, one obtainsMTT=MT1v−MT1a−Td  (8)
Briefly, there is a difference of two times between the times from the inlet of the capillary vessel to the respective barycenters of the tissue and the vein (refer to FIG. 10). This is based on a model in which the response function of the tissue is of a box type.
The barycentric time MTT of TIC: C(t) is generally calculated by
                    MTT        =                              ∫            0            ∞                    ⁢                                    tC              ⁡                              (                t                )                                      ⁢                                                  ⁢                                          ⅆ                t                            /                                                ∫                  0                  ∞                                ⁢                                                      C                    ⁡                                          (                      t                      )                                                        ⁢                                                                          ⁢                                      ⅆ                    t                                                                                                          (        9        )            
As described in Meier P, Zierler. K et al., “Journal of APPLIED PHYSIOLOGY” Volume 6, June 1954, 731-744, the definition by Zierler, “the output region from a tissue, i.e. the barycenter of TIC in a vein is defined MTT,” that is,MTT=MT1v  (10)is a definition in the case where the time that a contrast medium is rapidly infused into the inlet of a capillary wall in the tissue is assumed to be zero (case 1 in FIG. 9)
In the case where a contrast medium is infused through a cubital vein (case 2 in FIG. 9) as in an actual inspection, for example, when Ca(t) is measured at a carotid artery, Td varies with tissues depending on the control blood vessel of the brain and inputted Ca(t) expands during pulmonary circulation. Accordingly, the expression of Zierler cannot be used in its form.
The vein TIC has not model dependence but the tissue TIC has model dependence for the barycentric time, in both of which the barycenter of the artery TIC must be determined for quantification.
(Calculating CBF, CBV, and MTT by Maximum Gradient Method)
(Principle of Maximum Gradient Method)
As has been described, the expression of Fick is expressed asdCi(t)/dt=f●{Ca(t)−Cv(t)}  (11)wherein when the time of interest is time before the contrast medium flows into a vein and is shorter than the mean transit time of the tissue, or t<MTT, the following expression holds:Cv(t)≅0  (12)
Thus, the expression of Fick becomesdCi(t)/dt=f●Ca(t) (t<MTT)  (13)
When formula (13) is further differentiated by time, it is expressed asd2Ci(t)/dt2=f·dCa(t)/dt  (14)
As shown in FIG. 11, at time t=tmax.grad. when Ci (t) has the maximum slope at rise time, formula (14) becomesd2Ci(tmax.grad.)/dt=0from the relation f>0, the right side of formula (14) becomesdCa(tmax.grad)/dt=0
Since TIC is an upward convex curve, Ca(t) becomes a maximum value: Camax at t=tmax.grad. Thus the following relation holds:Ca(tmax.grad)=Camax formula (13) is thus transformed to calculate blood flow f by the expressionf={dCi(tmax.grad)/dt}/Camax  (15)
The maximum gradient method is based on the assumption that no contrast medium flows into a vein at t=tmax.grad. Accordingly, the assumption does not hold when the time width of a bolus infusion (input artery of the tissue) of input function is long. Accordingly, the assumption failure cannot sometimes be ignored for patients of poor pulmonary circulation. Even if Ci(t) and Ca(t) have delay time (refer to FIG. 12), Camax is not influenced by the delay time. Since CBF is calculated by the maximum gradient of TIC, the influence of the delay time is smaller than that by the method of calculating CBF from MTT and CBV without taking in consideration of the influence of delay time.
Also the deconvolution method used in the actual X-ray CT scanners in which Ca(t) is measured to obtain the response function of a tissue cannot ignore the influence of the delay time. They both have their own advantages and disadvantages case by case.
dCi(tmax.grad)/dt can be calculated as the first inflection point when it is approximated by gamma-variate function (refer to FIG. 10).
(Summary)
It is therefore difficult in DSC-MRI to measure artery TIC: Ca(t) accurately because linearity between index deltaR2* and the intensity of a contrast medium has not been proved and so high-intensity medium cannot ensure a dynamic range because of noises. With the reported “deconvolution method”, unless measured artery TIC: Ca(t) is in the close vicinity of a control tissue, the delay time (refer to Td of FIG. 12) from the measured region to the tissue is not corrected sufficiently, thus causing an error.
Although the method of obtaining the absolute value of blood flow by the maximum gradient method is easier than the centroid method, it needs the measurement of artery TIC: Ca(t), having many conditions that the time width of Ca(t) must be shorter than tissue MTT and as such, the quantitativity is questioned.